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Bootstrapping

Strongly Recommended Prerequisites

Recommended Prerequisites

In classical statistics, confidence intervals and hypothesis tests rely on making distributional assumptions about the data generating process. Often, these assumptions are incorrect. The bootstrap and related techniques rely on resampling from the data to construct the required distributions, and thus they are guaranteed to be correct given sufficient data. These techniques don't work very well with a small number of data points, but they are extremely effective in the era of big data.

Recommended Books

An Introduction to the Bootstrap

Bradley Efron and Robert J. Tibshirani

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Key Features

In-text exercises

Key Topics

Adaptive Estimation

Approximate Likelihoods

Bootstrap Confidence Intervals

Bootstrap Estimate of Bias

Bootstrap Estimate of Standard Error

Bootstrap Hypothesis Testing

Bootstrap for Regression Models

Connections Between the Bootstrap and Classical Inference

Cross Validation

Efficient Bootstrap Computation

Error in Bootstrap Estimates

Geometry of the Bootstrap

Parametric Bootstrap

Permutation Tests

Plug-In Principle

Practical Considerations When Using the Bootstrap

The Jackknife

Description

This is a great introduction to the bootstrap from its creator. It's quite gentle as statistical books go; the more challenging mathematics are relegated to the end of the book. Bootstrap hypothesis testing and confidence intervals receive excellent coverage, along with permutation testing, the jackknife, and other bootstrap-related topics. There is code that is written in the now largely defunct S language (the progenitor of R). It translates easily to R.